On the virial coefficients of confined fluids: Analytic expressions for the thermodynamic properties of hard particles with attractions in slit and cylindrical pores to second order

2019 ◽  
Vol 150 (4) ◽  
pp. 044704 ◽  
Author(s):  
William P. Krekelberg ◽  
Nathan A. Mahynski ◽  
Vincent K. Shen
Keyword(s):  
Thermodynamic Properties ◽  
Virial Coefficients ◽  
Second Order ◽  
Confined Fluids ◽  
Hard Particles ◽  
Cylindrical Pores ◽  
Analytic Expressions

Introduction

1984 ◽  
Author(s):  
C. G. Gray ◽  
K. E. Gubbins
Keyword(s):  
Thermodynamic Properties ◽  
Thermodynamic Functions ◽  
Energy Levels ◽  
Virial Coefficients ◽  
Intermolecular Forces ◽  
Great Accuracy ◽  
Perfect Gas ◽  
Mathematical Basis ◽  
Virial Series ◽  
Simple Molecules

The application of statistical mechanics to the study of fluids over the past fifty years † or so has progressed through a series of problems of gradually increasing difficulty. The first and most elementary calculations were for the thermodynamic functions (heat capacities, entropies, free energies, etc.) of perfect gases. These properties are related to the molecular energy levels, which for perfect gases can be determined theoretically (by quantum calculations) or experimentally (by spectroscopic methods, for example). For simple molecules (CO2 , CH4 , etc.) the energy levels, and hence the thermodynamic properties, can be determined with great accuracy, and even for quite complex organic molecules it is now possible to obtain thermodynamic properties with satisfactory accuracy. With the advent of digital computers it became possible to calculate thermodynamic properties for a wide variety of substances and temperatures, and several useful tabulations of perfect gas properties now exist. Having successfully treated the perfect gas, it was natural to consider gases of moderate density, where intermolecular forces begin to have an effect, by expanding the thermodynamic functions in a power series (or virial series) in density. Although the mathematical basis for a theoretical treatment of this series was laid by Ursell in 1927, it was not exploited until ten years later, when Mayer re-examined the problem. Since that time a great deal of effort has been put into evaluating the virial coefficients that appear in the series for a variety of intermolecular force models. As the expressions for the virial coefficients are exact, they provide a very useful means of checking such force models by comparison of calculated and experimental coefficients. While the theory of dilute gases at equilibrium is essentially complete, this is far from being the case for all dense gases and liquids. The virial series cannot be applied directly to liquids. As an alternative to the ‘dense gas’ approach to liquids, there were early attempts to treat liquids as disordered solids by using cell or lattice theories; these were popular from the mid-1930s until the early 1960s.

THERMAL PROPERTIES AND GROUND STATE ENERGY SHIFT OF CHARGED ANYONS

1994 ◽  
Vol 09 (20) ◽  
pp. 3683-3705
Author(s):  
J.Y. KIM ◽  
Y.S. MYUNG ◽  
S.H. YI
Keyword(s):  
Coulomb Interaction ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Correlation Energy ◽  
Virial Coefficients ◽  
Energy Shift ◽  
Second Order ◽  
Quantization Scheme ◽  
Coulomb Interactions

We derive the second and third virial coefficients and the ground state energy shift for charged anyons within the Hartree-Fock approximation. A second quantization scheme at finite temperature is introduced for this calculation up to the second order and the vertex is composed of anyonic, point, constant as well as Coulomb interactions. The thermodynamic potential for the second order correlation diagram of Coulomb interaction leads to the logarithmic divergence (V ln V). Hence, we find the heat capacity and the correlation energy of anyons without Coulomb-Coulomb interaction. Finally, we discuss the magnetic-field-induced localization at low filling ν, including the Wigner crystal phase.

scholarly journals Corrigendum to “second order virial coefficients from phase diagrams.” [Food Hydrocolloids 101 (2020) 105546]

2021 ◽  
Vol 112 ◽  
pp. 106324
Author(s):  
Belinda P.C. Dewi ◽  
Erik van der Linden ◽  
Arjen Bot ◽  
Paul Venema
Keyword(s):  
Phase Diagrams ◽  
Virial Coefficients ◽  
Second Order

Structural and thermodynamic properties of inhomogeneous fluids in rectangular corrugated nano-pores

2021 ◽  
Author(s):  
Yanshuang Kang ◽  
Haijun Wang ◽  
Zongli Sun
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Density Functional ◽  
Pore Geometry ◽  
Confined Fluids ◽  
Functional Theory ◽  
Slit Pores ◽  
Geometric Elements ◽  
Shed Light

Abstract Based on free-energy average method, an area-weighted effective potential is derived for rectangular corrugated nano-pore. With the obtained potential, classical density functional theory is employed to investigate the structural and thermodynamic properties of confined Lennard-Jones fluid in rectangular corrugated slit pores. Firstly, influence of pore geometry on the adsorptive potential is calculated and analyzed. Further, thermodynamic properties, including excess adsorption, solvation force, surface free energy and thermodynamic response functions are systematically investigated. It is found that pore geometry can largely modulate the structure of the confined fluids, which in turn influences other thermodynamic properties. In addition, the results show that different geometric elements have different influences on the confined fluids. The work provides an effective route to investigate the effect of roughness on confined fluids. It is expected to shed light on further understanding about interfacial phenomena near rough walls, and then provide useful clues for design and characterization of novel materials.

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